II. Human Capital, Returns to Education and Experience

Transcription

1 II. Human Capital, Returns to Education and Experience 1. Investment in Education 1. Motivation and Basic Trends 2. Human Capital Theory a. Compensating Differentials and the Mincer Wage Equation b. Theoretical foundations of the Mincer model c. Extensions to the Mincer Model 3. Challenges to the Mincer Wage Equation

2 1.1 Motivation and Basic Trends Labour supply deals with quantities of labour supplied, but there is also a quality aspect to labour, which can be enhanced by investment in education o Literacy and numeracy are the first goals of education Investment in education have long been seen to be key to economic well-being and growth o Education policies are important instruments towards economic growth o Basic education is indeed subsidized in most industrialized countries o Moreover, schooling is compulsory until years of age in many countries o More recently, policies have also focused on the early childhood learning More highly educated workers are paid more than less educated workers o Why? o Why isn t everyone getting a Ph.D.?

3 The benefits of education are seen not only in term of a more productive workforce, but also in term a healthier population, a more political engaged one, and a happier one! o There are social as well as private returns to education In summary, we can motivate our study of human capital policy with three major worries of our times: economic growth, inequality and poverty. Human capital is not a magic bullet that will solve all social problems, but is a promising avenue for substantial social improvement.

4 Source: Heckman and Lafontaine (2007) Figure XIII. Educational Attainment Decompositions, Males and Females Birth Cohorts Percentage 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% Graduate HS Attend College Attend Given HS Graduate College Graduate Given Attend Year of Birth Notes: 3-year moving averages based on CPS October, Census, CPS March and NCES data. HS graduates are those who obtained a regular public or private HS diploma (excluding GEDs) from the NCES. "Graduate HS" is the fraction of 8th grade enrollments for a given cohort who report a regular HS diploma. "Attend Given HS" is the fraction of recent HS graduates who report being enrolled the fall of the year following graduation. "Attend College" is college enrollments of recent HS graduates as a fraction of 18 year old cohort size. College graduates are those who report a BA or higher by age 25. "Graduate Given Attend" is those who obtained a four year degree as a fraction of the college enrollment total for that cohort. Two-year degrees are not included. "Graduate College" is the number of college graduates as a fraction of the 18 year old cohort size. Population estimates are from the Census P-20 reports. HS diplomas issued by sex are estimated from CPS October data after 1982.

5 Source: Heckman and Lafontaine (2007) Percentage 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% Figure XIV. Educational Attainment Decompositions, Males Birth Cohorts Graduate HS Attend College Attend Given HS Graduate College Graduate Given Attend Year of Birth Notes: 3-year moving averages based on CPS October, Census, CPS March and NCES data. HS graduates are those who obtained a regular public or private HS diploma (excluding GEDs) from the NCES. "Graduate HS" is the fraction of 8th grade enrollments for a given cohort who report a regular HS diploma. "Attend Given HS" is the fraction of recent HS graduates who report being enrolled the fall of the year following graduation. "Attend College" is college enrollments of recent HS graduates as a fraction of 18 year old cohort size. College graduates are those who report a BA or higher by age 25. "Graduate Given Attend" is those who obtained a four year degree as a fraction of the college enrollment total for that cohort. Two-year degrees are not included. "Graduate College" is the number of college graduates as a fraction of the 18 year old cohort size. Population estimates are from the Census P-20 reports. HS diplomas issued by sex are estimated from CPS October data after 1982.

6 Source: Heckman and Lafontaine (2007) Figure XV. Educational Attainment Decompositions, Females Birth Cohorts Percentage 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% Graduate HS Attend College Attend Given HS Graduate College Graduate Given Attend Year of Birth Notes: 3-year moving averages based on CPS October, Census, CPS March and NCES data. HS graduates are those who obtained a regular public or private HS diploma (excluding GEDs) from the NCES. "Graduate HS" is the fraction of 8th grade enrollments for a given cohort who report a regular HS diploma. "Attend Given HS" is the fraction of recent HS graduates who report being enrolled the fall of the year following graduation. "Attend College" is college enrollments of recent HS graduates as a fraction of 18 year old cohort size. College graduates are those who report a BA or higher by age 25. "Graduate Given Attend" is those who obtained a four year degree as a fraction of the college enrollment total for that cohort. Two-year degrees are not included. "Graduate College" is the number of college graduates as a fraction of the 18 year old cohort size. Population estimates are from the Census P-20 reports. HS diplomas issued by sex are estimated from CPS October data after 1982.

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9 1.2. Human Capital Theory a. Compensating Differentials and the Mincer Wage Equation Human capital theory has emerged as a special case in the theory of equalizing or compensating wage differentials. The idea was first introduced by Adam Smith (1776) to explain the equilibrium between labour demand and labour supply. According the Smith, it is not the wage that is equated across jobs in a competitive market ( perfect liberty ), but the whole of the advantages and disadvantages of a job. The five following are the principal circumstances which, so far as I have been able to observe, make up for a small pecuniary gain in some employments, and counter-balance a great one in others: first, the agreeableness or disagreeableness of the employments themselves; second, the easiness and cheapness, or the difficulty and expence of learning them; third, the constancy or inconstancy of employment in them; fourth, the small or great trust which must be reposed in those who exercise them; and fitfthly, the probability or improbability of success in them.

10 The modern equivalent is: 1) undesirable work conditions, 2) human capital requirements, 3) job security, 4) responsibilities and 5) probability of success. Differences emerging from 1), 2), 4) and 5) are still is use today in job evaluation scheme of pay equity legislation and in administrative pay systems. 3) is partly addressed by the unemployment insurance. The basic idea is that an employer must pay a premium to get you to do some job that you don t like to do (e.g. pest control workers), and conversely he may get you at a discount if the job is like leisure to you (e.g. ski patrols) The key insight of Rosen s (1974) theoretical work on hedonic prices is that the implicit price of an attribute represents both the marginal valuation to customers and the marginal cost to firms. Hedonic are defined as the implicit prices of attributes or qualities and are revealed to economic agents from observed prices of differentiated products and the specific amounts of characteristics associated with them.

11 Job Evaluation Job Evaluation Systems Pay Equity Commission ontario.ca français Search GO HOME ABOUT US REVIEW SERVICES TRAINING RESOURCES CONTACT US Location: Pay Equity Commission > Resources > Job Evaluation Overview Resources General Information Guidelines Public Sector Pay Equity Plan Samples Best Practices Forms and Notices Case Studies and Tools Job Evaluation (JE)Systems Job evaluation systems must measure work in terms of Skill, Effort, Responsibility and Working conditions - these 4 factors are required by the Pay Equity Act. A job evaluation system is usually made up of the parts below. Subfactors These are elements of skill, effort, responsibility and working conditions significant to the types of work done in the workplace. At Space Toy Co., these 4 factors were expanded to include one to four subfactors each. For example, it was decided that the factor of Skill should include these three subfactors: Print Multilingual Pamphlets Skill E-Learning Modules: Pay Equity for Small Businesses Knowledge Interpersonal Skill Contacts Problem Solving Judgement The factors of Effort, Responsibility and Working conditions were similarly expanded to include a number (1 of 3) [1/27/2012 4:14:46 PM]

12 Job Evaluation Job Evaluation Systems Pay Equity Commission of subfactors. Levels Levels measure the degree of importance of that subfactor in each job. For example, when discussing the subfactor of Problem Solving/Judgement: The Committee felt there was a high degree of problem-solving and judgement required to perform most of the jobs at Space Toy Co., so they agreed to give this subfactor 5 levels. All of the subfactors in the system were given 4 to 6 levels each. Weighting Weighting is used to allocate points to factors, subfactors and levels. The total number of points in a system is divided among these three. For example, Space Toy Co.'s system had a total value of 100% / 1000 points. The Committee allocated percentages to the four factors in the following manner: Skill 35% (350 points) Effort 20% (200 points) Responsibilities 35% (350 points) Working Conditions 10% (100 points) They then expanded the formula further by dividing these percentages between the subfactors and the levels. (2 of 3) [1/27/2012 4:14:46 PM]

13 Product in a class are completely described by a vector of coordinates z ( z1, z2,., zn ) with price p( z) p( z1, z2,., zn ) determined by market clearing conditions: the amounts of commodities offered by sellers at every point in the hedonic space must equal amounts demanded by consumers choosing to locate there. Letting ( z; u, y) be the consumer s willingness to pay for z at a fixed utility index and income, the utility maximizing equilibrium will be characterized by * * * ( z ; u, y) p ( z ), i i 1,, n. z i * * * * The profit maximizing product designs will satisfy pi ( z ) z ( z1,., zn ;, ), for i i 1,,n, where ( z 1,., zn;, ) is the firm s offer function indicating unit prices (per model) the firm is willing to accept on various designs at constant profit when quantities produced of each model are optimally chosen. d s The market equilibrium is reached when there exists p (z), such that Q ( z) Q ( z), for all z, and buyers and sellers act as described above. That is, equilibrium is described by the intersection of supply and demand functions.

14 Source: Rosen (1974)

15 For a quadratic cost function and a linear utility function, Rosen (1974) shows that a closed form solution for p (z) exists. Recently, Ekeland, Heckman and Nesheim (2004) derive more general necessary conditions for identification. In the labour market theory of equalizing differences, a labour market transaction is viewed as a tied sale, where the worker simultaneously sells the services of his labour and buys the attributes of his job. The positive price the worker pays for preferred job activities is subtracted from the wage payment. Measurable job attributes on which compensating wage differential have been shown to arise empirically onerous risk conditions, such as risk to life and health, exposure to pollution, intercity or interregional wage differences associated with differences in climate, crime, pollution and crowding special work-time scheduling and related requirements, including shift work, inflexible work schedules, and possible risks of layoff and subsequent unemployment. the composition of pay packages, including vacations, pensions, and other fringe benefits as substitutes for direct cost payments.

16 The empirical analysis of less onerous job characteristics than risk of injury or death has been less successful. The theory of equalizing differences asserts that workers should receive compensating wage premiums when they accept jobs with undesirable nonwage characteristics. o Much of the empirical support however provides inconsistent support for the theory, with wrong-signed or insignificant estimates of the wage premiums fairly common. Hamermesh (1999) finds support for the argument that income effects lead to difficulties in measuring the price of a disamenity. o Since by definition the disamenity is an inferior good, a higher skilled worker s higher full earnings lead him to buy less of the disamenity. There is thus a negative correlation between full earnings, the combination of the wage and the disamenity, and the disamenity itself.

17 Of the five principal circumstances for which Adam Smith argued there should be compensating wage differentials, the second one was the easiness and cheapness, or the difficulty and expence of learning a business. But it is when he compared an educated human to an expensive machine that laid out the basics of human capital theory When any expensive machine is erected, the extraordinary work to be performed by it before it is workn out, it must be expected, will replace the capital laid out upon it, with at least the ordinary profit. A man educated at the expence of much labour and time to any of those employments which require extraordinary dexterity and skill, may be compared to one of those expensive machines.... It must do this too in a reasonable time, regard being had to the very uncertain duration of human life, in the same manner as to the more certain duration of the machine. The difference between the wages of skilled labour and those of common labour, is funded on this principles. With human capital theory, investments in human resources are considered similarly to other types of investments. Costs are incurred in expectation of future benefits and the investment in the last unit of human capital is made only if the benefits are expected to exceed the costs.

18 On the supply side: additional schooling entails opportunity costs in the form of foregone earnings plus direct expenses such as tuition. To induce a worker to undertake additional schooling, he must be compensated by sufficiently higher lifetime earnings. On the demand side: to command higher earnings, more schooled workers must be sufficiently more productive than their less schooled fellow workers. In the perfect competition framework, the wage guides the allocation of workers across firms as to achieve an efficient allocation of resources by equating the wage to the value of the marginal product. In the long run equilibrium, the relationship between lifetime earnings and the schooling must be such that i) the supply and demand for workers of each schooling level are equated and ii) no worker wishes to alter their schooling level.

19 b. Theoretical foundations of the Mincer model The study of the effects of investment in schooling and on-the-job training on the level, pattern and interpersonal distribution of life-cycle earnings have been pioneered by Becker (1964, 1975) and Mincer (1958, 1962, 1979). This lead to one of the more successful empirical equation called the Mincer earnings function 2 ln( w ) 0 rs 1E 2E, where w is earnings (or the hourly wage when available), S is years of schooling, E is years of labor market experience, and is an error term. Years of schooling are a fairly direct measure of education human capital, while years of labour market experience is viewed as a proxy for on-the-job training. Mincer uses the transformation Experience equals Age minus Schooling minus 6, E A S 6, to capture the interaction between schooling and experience, but assumes multiplicative separability.

20 1104 Journal of Economic Literature, Vol. XXXIX (December 2001) A. United States B. Sweden Source: Krueger and Lindahl 10 - ~ ~ ~ ~ 05-, _,_, _, _, _,_,_,_,_,_,, 3.5-, _._._._._._._._._ Years of Schooling Years of Schooling C. West Germany D. East Germany ~~~~~~~~~~~ l 7,,,,,6 A _ Years of Schooling Years of Schooling Figure 1. Unrestricted Schooling-Log Wage Relationship and Mincer Earnings Specification

21 The Mincer equation thus captures the important empirical regularities: 1) increase in earnings with schooling, 2) concavity of log earnings in experience, 3) log earnings experiences profiles are parallel across different education groups (ratio of earnings for persons with education levels differing by a fixed number of years is roughly constant across schooling levels) no interaction between schooling and experience 4) log earnings-age profiles diverge across different education groups. Almost all empirical studies find that schooling has a positive and significant effect on earnings ( r 0 ) that earnings are a concave function of labour market experience ( 1 0 and 2 0). A simple regression model with a linear schooling term and a low-order polynomial in potential experience explains 20-35% of the variation in observed earnings data, with predictable and precisely-estimated coefficients in almost all applications.

22 Source: Lemieux (2001) Figure 1 Source: Jacob Mincer, Schooling, Experience, and Earnings

23 The theoretical foundations of Mincer specification can arise from two theoretical framework, i. compensating wage differentials (Mincer, 1958) ii. accounting identity framework (Mincer, 1974). Let w (s) represent the annual earnings of a representative individual with s years of education, and let r be the discount rate, both assumed to be constant over his lifetime, the present value of the stream of earnings (for infinitely lived individuals) is PV(s) = w(s) + () () () = w(s) + () () () () = w(s) () Assuming no direct costs of schooling and comparing an individual with 1 year of schooling, who has to wait that one year before earning a salary, to one with 0 year of schooling, and equalizing present values, we get w(1) 1 + r 1 w(1) = = w(0) 1 + r r 1 + r r r w(1) w(0) = 1 + r

24 Taking the logarithm on both side, lnw(1) ln (w(0)) = ln (1 + r) r for r < 0.2 the wage increment for one more year of schooling must approximately be equal to the rate r! Or in continuous time, let w (s) represent the annual earnings of a representative individual with s years of education, T V ( s) e s rt w( s) r where T is the length of working time. w( s) dt Letting the compensating differentials take their time to equalize lifetime earnings: V ( s) V (0) ln( V ( s)) ln( V (0)) e rs e rt

25 The earnings difference between an individual with s years of schooling and 0 years will be given by rt r( T s) ln w( s) ln w(0) rs ln (1 e ) /(1 e ) ln w(0) rs, since the last term goes to zero as T gets large. This yields the nice interpretation of r as an internal rate of return to schooling, that is, the discount rate equates the lifetime earnings streams from different educational choices. But this framework ignores the direct costs of schooling, assumes that earnings do not vary over the life-cycle, and that the age of retirement does not depend on years of schooling. An alternative framework used by Mincer (1974) builds on an accounting identity initially studied by Becker (1974) and Becker-Chiswick (1966). It allows earnings to vary over the life-cycle!

26 Let E t be potential earnings at time t. Investments in training are expressed as a fraction of potential earnings invested, Ct kt Et, where k t is the fraction invested at time t and let t be the return to training investments made at time t. Then E E C E k t1 t t t t 1 t t. Repeated substitution yields t j j 0 E t 1 1 k E j 0. Formal schooling is defined as years spent in full-time investments ( k t 1). Assume that the rate of return on formal schooling is constant ( t s ) and that formal schooling takes place at the beginning of life. Also assume that the rate of return to post-school investment, t, is constant over time and equals 0. Then, we can write (in logs) ln E t ln E S ln(1 ) 0 s js t 1 ln(1 k 0 j ),

27 Which yields the approximate relationship (for small s and 0 ) using the fact that ln( 1 ), if 0. 2, ln E ln E S t k j js To establish a relationship between potential earnings and years of labour market experience, Mincer (1974) further assumes a linearly declining rate of post-school investment: x k s x (1 ), T where x t s 0 is the amount of work experience as of age t and T is the length of working life. Under these assumptions, the relationship between potential earnings, schooling and experience is given by: ln Ex s ln E0 0 ss 0 x x. 2T 2T t 1.

28 Observed earnings equal potential earnings less investment costs, producing the following relationship for observed earnings: T x E x s w s x 1 ln ), ( ln ln ), ( ln x T x T T s E x s w s x x s s When s E and are uncorrelated, the variance of log earnings will be minimized at 0. / 1. (See Heckman et al.)

29 Source: Gunderson et al. (2006)

30 c. Extensions to the basic Mincer model In most applications of the Mincer model, it is assumed that the intercept and slope coefficient are the same across persons and do not depend on the schooling level, however allowing and s to differ across persons, as in Mincer (1974) produces a random coefficient model 2 2 ln w( s, x) 0 ss 1x 2x ( 0i 0 ) ( si s ) s ( 1 i 1) x ( 2i 2 ) x, where the terms in bracket are part to the error term, expressed in deviations from the mean coefficients. It turns out that this is a crucial extension to the basic model. Since if individuals were identical, why should they choose different amounts of education? However, although heterogeneity explains why we observe different individuals having different schooling, an additional set of problems is introduced: Schooling is endogeneous and, if this is not allowed for, estimated return may be biased. Returns as well as schooling may vary across individuals.

31 This will have important implications (see, Card (1999)) for the econometric estimation of the Mincer equation, which we will talk about in the estimation section. Other extensions to the Mincer model: Heckman, Lochner and Todd (2003, 2008) examine the importance of relaxing functional form assumptions in estimating internal rates of return to schooling and in accounting for taxes( ), tuition ( v ), independence of the length of work-life from schooling ( T ( s) 1), nonlinearity in schooling, and non-separability between schooling and work experience( w( s, x) u( s) ( x) ): V ( s) T ( s) s e (1 ) r( xs) w( s, x)(1 ) dx 0 0 s ve (1 ) rz Inferences about trends in rates of return to high school and college obtained from the more general model differ substantially from inferences drawn from estimates based on the basic Mincer earnings regression. dz,

32 Heckman et al. also examine the implications of accounting for uncertainty and agent expectation formation. Even when the static framework of Mincer is maintained, accounting for uncertainty substantially affects rate of return estimates. They propose a substantial break from Mincer's approach by allowing for the sequential resolution of uncertainty. That is, with each additional year of schooling, information about the value of different schooling choices and opportunities becomes available generating an option value of schooling. The return in excess of the direct return (the lifetime income received at a given schooling level) is the option value. For example, finishing high school provides access to college, and attending college is a necessary first step for obtaining a college degree. Each additional year of schooling reveals new information about uncertain college costs or future earnings. Individuals with s years of schooling must decide whether to quit school and receive lifetime earnings of Y (s), or continue on in school for an additional year and receive an expected lifetime earnings of E s ( V ( s 1)).

33 When the schooling decision is made at the beginning of life and age-earnings streams across schooling levels are known and cross only once, then the internal rate of return (IRR) can be compared with the interest rate as a valid rule for making education decisions (Hirschleifer, 1970). But the sequential resolution of uncertainty and non-linearity in returns to schooling contribute to sizeable option values. Accounting for option values challenges the validity the internal rate of return. They conclude that in the presence of sequential resolution of uncertainty and option values, the internal rate of return-a cornerstone of classical human capital theory-is not a useful guide to policy analysis.

34 3. Challenges to the Mincer Wage Equation The basic Mincer human capital earnings function does not appear to fit the data nearly as well in the 1980s and 1990s as it did in the 1960s and 1970s: 1) Log wages are an increasingly convex function of years of schooling: that is, the log-linearity in schooling no longer seems to hold. 2) The quadratic in experience tends to understate earnings growth at the beginning of the lifecycle and overstate the decline in earnings towards to the end of the lifecyle. Murphy and Welch (1990) find that a quartic fits the data better.

35 Source: Lemieux (2001)

36 Source: Lemieux (2001)

37 Source: Lemieux (2001)

38 3) Experience-wage profiles are no longer parallel for different education groups: that is, the multiplicative separability between experience and schooling no longer holds. For example, the college-high school wage gap is now much larger for less experienced than for more experienced workers. The Mincer model is for individuals tracked over school and working ages, and should be estimated by tracking single cohorts through education and the labour market. But it is usually estimated from a cross-section of individuals, which is actually only legitimate if the economy is in a long run steady state. Rapid technical change or secular improvement in the quality of education would violate this assumption and invalidate the use of cross-sectional data for estimation: cross-section and cohort based estimates of returns to education would not be expected to be the same. Mincer was well aware that this may be a problem in his early work (Mincer, 1958), and conjectured that the cross-sectional age-earnings profiles were probably

39 understating life-cycle earnings growth since, in those days, there was substantial secular growth in average earnings. Now many researchers believe that the cross-sectional age-earnings profile overstates life-cycle earnings growth. Beaudry and Green (2000) conclude that the slope of the cross-sectional age-earnings profile has increased because new cohorts of men are entering the labour market at increasingly low earnings level in Canada. This highlights the well-known problem of distinguishing between age, cohort, and year effects in earnings growth. Card and Lemieux (2001) investigate this issue in detail and conclude that the dramatic increase in the college-high school wage gap for post-1950 cohorts is primarily a consequence of an equally dramatic break in inter-cohort trends in educational achievement. Until 1950, each successive cohort of men was more educated than the preceding cohort. This secular trend abruptly stopped with men born around 1950.

40 920 P. Beaudry and D. Green a}~~~~~~~~~~~~~~~ n 1982 Entry -- 19B6 Entry 350 S * 1990 Entry 990 Cross Section 300 ' ' ' ' FIGURE 3b Age-earnings profiles allowing differing slopes by cohort: males, university education Age

41 After 1975, the entry of the post-1950 cohorts were no more educated, and in some case less educated, than previous cohorts. o The relative supply could no longer offset the rising demand for skilled young workers and, as a result, the college-high school wage gap started expanding dramatically for young workers.

42 Take-Away In summary, recent evidence suggests that the basic Mincer human capital earnings model remains a parsimonious and accurate model in a stable environment where educational achievement grows smoothly across cohorts, as it did in the time period originally studied by Mincer (1974). In a less stable environment, however, major shifts in the relative supply of different age-education groups can induce important changes in the structure of wages that have to be taken into account when estimating a standard Mincer equation. How to interpret the coefficient on schooling? o Ability bias: Upward bias o Heterogeneity in effects:??? o Measurement Error: Downward bias o Signalling vs. Human Capital

43 Basic readings: Card, D. The Causal Effect of Education on Earnings, in Ashenfelter, O.C. and D. Card, editors, Handbook of Labor Economics, North-Holland, Vol. III A,1999. Heckman, J.J., L. J. Lochner and P.E. Todd, Fifty Years of Mincer Earnings Regressions, NBER WP 9732, May Lemieux, T. The Mincer Equation Thirty Years after Schooling, Experience, and Earnings, Center for Labor Economics, University of California-Berkeley, WP No. 62, October 2003.